A Remark on the Steklov–Poincaré Inequality

Sh. M. Nasibov

Institute of Applied Mathematics, Baku State University

Abstract: In an $n$-dimensional bounded domain $\Omega_n$, $n\ge 2$, we prove the Steklov–Poincaré inequality with the best constant in the case where $\Omega_n$ is an $n$-dimensional ball. We also consider the case of an unbounded domain with finite measure, in which the Steklov–Poincaré inequality is proved on the basis of a Sobolev inequality.

Keywords: Steklov's inequality, Poincaré inequality, Sobolev inequality, best constant.

UDC: 517.518

Received: 05.02.2021

DOI: 10.4213/mzm13196

 English version: Mathematical Notes, 2021, 110:2, 221–225

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